rate*time=distance

A passenger train and a freight train start at 405 miles apart and travel towards each other. the rate of the passenger train is twice the rate of the freight train. in 3 hours they pass each other (or collide). how fast are they going?

A passenger train and a freight train start at 405 miles apart and travel towards each other. the rate of the passenger train is twice the rate of the freight train. in 3 hours they pass each other (or collide). how fast are they going?

Pet Peeve Warning!!! Danger Will Robinson! Danger! Danger!

Why can't Math books just use the term "speed" like everyone else? "rate*time = distance." "rate" of what, I ask you???

Pet Peeve over.

Okay. Let's assume that the passenger train starts from the left and the freight train starts from the right. For the record I am going to set an origin at the starting position of the passenger train and set the +x direction to be to the right.

The passenger train will move with a speed and cover a distance x miles. The freight train will move with a speed and covers a distance 405 - x miles. They meet at the same time, t = 3 hours.

A passenger train and a freight train start at 405 miles apart and travel towards each other. the rate of the passenger train is twice the rate of the freight train. in 3 hours they pass each other (or collide). how fast are they going?

Let s be the speed of the frieght train.
Then the speed of the passenger train is 2s.